Solve the congruence: 1287x ≡ 447 (mod 516)

Expert Solution

Colby Messinger answered 2 years ago

Solve the the congruence 11x 4 (mod 26) Use the Lucas-Lehmer Test to show that 127...

Solve the the congruence 11x 4 (mod 26) Use the Lucas-Lehmer Test to show that 127 = 2^7-1 is prime. Use the Lucas-Lehmer Test to show that 2047 = 2^11- 1 is not prime Use the Lucas-Lehmer Test to show that 8191 = 2^13 - 1 is prime. Assume Alice uses the following information to develop the public key, N, in an SS Cryptosystem: p = 23 and q = 41 with N = p2q = 21689. Suppose Bob wants...

A. Find all the solutions for the congruence ax ≡ d (mod b) a=123, b=456, d=3

Solve a system of equations: 1- 2x = 5 mod 15 3x = 1 mod 4...

Solve a system of equations: 1- 2x = 5 mod 15 3x = 1 mod 4 2- x = 5 mod 15 x = 2 mod 12 (Hint: Note that 15 and 12 are not relatively prime. Use the Chinese remainder theorem to split the last equation into equations modulo 4 and modulo 3)

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21)...

Solve the following system of congruences: x ≡ 2 (mod 14) x ≡ 16 (mod 21) x ≡ 10 (mod 30)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19)

1. Use backward substitution to solve: x=8 (mod 11) x=3 (mod 19) 2. Fine the subgroup of Z24 (the operation is addition) generates by the element 20. 3. Find the order of the element 5 in (z/7z)

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod...

0 mod 35 = 〈0 mod 5, 0 mod 7〉 12 mod 35 = 〈2 mod 5, 5 mod 7〉 24 mod 35 = 〈4 mod 5, 3 mod 7〉 1 mod 35 = 〈1 mod 5, 1 mod 7〉 13 mod 35 = 〈3 mod 5, 6 mod 7〉 25 mod 35 = 〈0 mod 5, 4 mod 7〉 2 mod 35 = 〈2 mod 5, 2 mod 7〉 14 mod 35 = 〈4 mod 5, 0 mod 7〉...

Question 6 A random sample of 516 U.S. businesses found that 144 of the 516 businesses...

Question 6 A random sample of 516 U.S. businesses found that 144 of the 516 businesses had fired workers for misuse of the Internet. A 90% confidence interval for the proportion of all U.S. businesses who have fired workers for misuse of the Internet is between Blank-1 and Blank-2

Use the Extended Euclid's Algorithm to solve ƒ-1 for 8 mod 11

Using the Chinese remainder theorem solve for x: x = 1 mod 3 x = 5...

Using the Chinese remainder theorem solve for x: x = 1 mod 3 x = 5 mod 7 x = 5 mod 20 Please show the details, I`m trying to understand how to solve this problem since similar questions will be on my exam.

a. Solve 7x + 5 ≡ 3 (mod 19). b. State and prove the Chinese Remainder Theorem

a. Solve 7x + 5 ≡ 3 (mod 19). b. State and prove the Chinese Remainder Theorem c. State and prove Euler’s Theorem. d. What are the last three digits of 9^1203? e. Identify all of the primitive roots of 19. f. Explain what a Feistel system is and explain how to decrypt something encoded with a Feistel system. Prove your result.

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